Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-05-24
Physics
High Energy Physics
High Energy Physics - Theory
ACTA MATHEMATICA (to appear); finalised version with a note of clarification regarding the connection of the commensurability
Scientific paper
There exists on each Teichm\"uller space $T_g$ (comprising compact Riemann surfaces of genus $g$), a natural sequence of determinant (of cohomology) line bundles, $DET_n$, related to each other via certain ``Mumford isomorphisms''. There is a remarkable connection, (Belavin-Knizhnik), between the Mumford isomorphisms and the existence of the Polyakov string measure on the Teichm\"uller space. This suggests the question of finding a genus-independent formulation of these bundles and their isomorphisms. In this paper we combine a Grothendieck-Riemann-Roch lemma with a new concept of $C^{*} \otimes Q$ bundles to construct such an universal version. Our universal objects exist over the universal space, $T_\infty$, which is the direct limit of the $T_g$ as the genus varies over the tower of all unbranched coverings of any base surface. The bundles and the connecting isomorphisms are equivariant with respect to the natural action of the universal commensurability modular group.
Biswas Indranil
Nag Subhashis
Sullivan Dennis
No associations
LandOfFree
Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms Over the Universal Commensurability Teichmüller Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms Over the Universal Commensurability Teichmüller Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms Over the Universal Commensurability Teichmüller Space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-408729